{"paper":{"title":"A multiparameter semipositone fractional laplacian problem involving critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"R. Dhanya, Sweta Tiwari","submitted_at":"2019-05-24T07:06:16Z","abstract_excerpt":"In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type\n  $$ (P_\\lambda^\\mu)\\left\\{ \\begin{array}{lll} (-\\Delta)^s u&=& \\lambda(u^{q}-1)+\\mu u^r \\mbox{ in } \\Omega\\\\ u&>&0 \\mbox{ in } \\Omega\\\\ u&\\equiv &0 \\mbox{ on }{\\mathbb R^N\\setminus\\Omega}. \\end{array}\\right. $$ when the positive parameters $\\lambda$ and $\\mu$ belongs to certain range. Here $\\Omega\\subset\\mathbb R^N$ is assumed to be a bounded open set with smooth boundary, $s\\in (0,1), N> 2s$ and $0<q<1<r\\leq \\frac{N+2s}{N- 2s}.$ The proof relies on the construction of a positi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10062","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}